A method for selecting model parameters based on accuracy and computational feasibility criteria

DOI: 10.31673/2412-9070.2026.318101

Abstract

This paper provides a formal description of an algorithm for determining the feasible domain of admissible parameters for a discrete mathematical model of acoustic wave propagation in validation tasks based on field measurements. The key practical challenge addressed by the algorithm is the need to satisfy several requirements simultaneously: numerical correctness of the simulation, computational feasibility under limited resources, and sufficient agreement between simulation outputs and experimental observations according to a predefined accuracy metric. In typical validation work-flows, increasing numerical resolution or model detail can improve accuracy, but it also increases runtime and memory consumption, which makes many configurations impractical for repeated runs and parameter studies. Therefore, a systematic and reproducible procedure is required to identify the set of parameter configurations that meets the target accuracy while remaining feasible on the available hardware.
The proposed algorithm is based on sequential selection (filtering) of parameter configurations according to a cascade of criteria. First, configurations are checked for numerical correctness to exclude those that violate stability or other validity conditions and may lead to non-physical results or divergence. Second, for configurations that pass the numerical filter, computational resources are measured (execution time and, if available, memory usage) and compared with predefined limits to ensure resource feasibility. Third, the accuracy of the model output is evaluated by comparing simu-lated signals with experimental measurements using a specified metric, and only configurations that satisfy the accuracy threshold are retained. If required, the algorithm includes an additional self-consistency verification step: the results of a candidate configuration are compared with a control computation of higher numerical accuracy (e.g., using refined discretization) in order to reject configurations that do not demonstrate acceptable convergence.
As a result, the algorithm produces a set of admissible parameter configurations that simultaneously satisfies hardware constraints and provides the required accuracy, thereby forming a practical basis for reproducible and interpretable parameter selection in software tools for validation of acoustic wave propagation models.

Keywords: mathematical model validation, acoustic wave propagation, discrete model, model parameters, admissible parameter domain, numerical correctness, computational feasibility, accuracy metric, self-consistency, configuration selection algorithm.